Finite deformation is the principal actuation basis of elastomer-based pneumatic soft actuators. Desired deformation behavior is the key design requirement for such actuators. The objective of current study is to optimize the design of a flat shell gripper and to investigate its interaction with a cylindrical object. Herein, we propose an analytical model for a membrane-based flat shell gripper. The model is based on finite strain membrane theory and neo-Hookean material. The proposed model considers the contact interaction of the actuator with flat and cylindrical rigid substrates. The model is developed for three different states of the actuator: 1) free-space; 2) contact with a flat substrate; and 3) contact with a cylindrical substrate. In application, the model was used to predict the relative position and air pressure required to grasp a cylindrical object by a parallel two-fingered shell gripper. Additionally, the frictional behavior of the actuator in contact with a cylindrical substrate is investigated. The model involves only solving nonlinear algebraic equations and is computationally efficient. The theoretically predicted deformation behavior of the actuator is experimentally validated via free-space deformation, force measurement, and grasping tests.